Question

Given the formula nt =. find the time it would take to double an initial deposit of $3,000 at an interest rate of 5.25%, compounded semi-annuallylog(1 + -(rounded to the nearest whole year).16 years15 years18 years13 yearsNone of these choices are correct.

Answer 1

The Solution.

For the initial deposit of $3,000 to double it, means the amount will become $6,000.

Semi-annually implies 2 periods in a year.

The given formula is

`nt=\frac{\log_{}((FV)/(P))}{\log_{}(1+(r)/(n))}`
`\text{Where n=2, FV=\$6000, P=\$3000, r=0.0525, t=?}`

substituting these values, we get

`2t=\frac{\log _{}((6000)/(3000))}{\log _{}(1+(0.0525)/(2))}`
`2t=\frac{\log _{}2}{\log _{}(1+0.02625)}`
`2t=\frac{\log _{}2}{\log _{}(1.02625)}=(0.3010)/(0.01125)=26.7556`
`\begin{gathered} \text{Dividing both sides by 2, we get} \\ t=(26.7556)/(2)=13.3778\approx13\text{ years} \end{gathered}`

Therefore, the correct answer is 13 years (4th option)